We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré-Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.
Fonda, A., Garrione, M., Gidoni, P. (2016). Periodic perturbations of Hamiltonian systems. ADVANCES IN NONLINEAR ANALYSIS, 5(4), 367-382 [10.1515/anona-2015-0122].
Periodic perturbations of Hamiltonian systems
GARRIONE, MAURIZIO;
2016
Abstract
We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincaré-Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.
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